Due to the broadcast nature of wireless communications systems, such as spread spectrum communications, radar, mobile device communications, etc., communicating devices need to differentiate between and/or synchronize with signals being transmitted by other devices in a given proximity. One way this can be accomplished is by applying sequences to data transmitted over a wireless communication system such that a receiver of the data can differentiate signals of disparate devices based on the sequences. In this regard, sequences with good aperiodic auto-correlation functions (ACF), such as Barker sequences, can be used to facilitate improved sequence recognition. Additionally, utilization of low correlation windows in the ACF has been suggested for synchronizing signals during data transmission; these sequences have a window centralized around an in-phase position where correlation sidelobes are minimized to satisfy the Barker condition. The aperiodic ACFs are considered when computing desired sequences achieving the largest window around the main lobe. Moreover, as signal propagation delays and other factors, such as inaccurate timing due to the use of low-cost oscillators, affect the ability to provide perfect synchronization among communicating devices, approximately synchronous or quasi-synchronous code division multiple access (QS-CDMA) systems have also been proposed restricting delay between users within one or a few chips.
Even so, the multipath delay spread can reach values such that additional mechanisms are required to mitigate interference caused by the delay spread. For example, the spread can be larger than half of the correlation zone, since the correlation value outside the conventional single low correlation zone is not constrained.